Q1: What is \(2\frac{1}{4} + 1\frac{1}{4}\)? (a) \(3\frac{1}{2}\) (b) \(3\frac{2}{4}\) (c) \(3\frac{1}{4}\) (d) \(4\frac{1}{4}\)
Solution:
Ans: (a) Explanation: Add the whole numbers: \(2 + 1 = 3\). Add the fractions: \(\frac{1}{4} + \frac{1}{4} = \frac{2}{4}\). Simplify \(\frac{2}{4} = \frac{1}{2}\). So the answer is \(3\frac{1}{2}\).
Q2: What is \(5\frac{3}{5} - 2\frac{1}{5}\)? (a) \(3\frac{1}{5}\) (b) \(3\frac{2}{5}\) (c) \(3\frac{4}{5}\) (d) \(4\frac{2}{5}\)
Solution:
Ans: (b) Explanation: Subtract the whole numbers: \(5 - 2 = 3\). Subtract the fractions: \(\frac{3}{5} - \frac{1}{5} = \frac{2}{5}\). The answer is \(3\frac{2}{5}\).
Q3: What is \(4\frac{1}{3} + 2\frac{2}{3}\)? (a) \(6\frac{3}{3}\) (b) \(7\) (c) \(6\frac{1}{3}\) (d) \(6\frac{2}{3}\)
Solution:
Ans: (b) Explanation: Add the whole numbers: \(4 + 2 = 6\). Add the fractions: \(\frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1\). Add the extra whole number: \(6 + 1 = 7\).
Q4: When subtracting \(5\frac{1}{6} - 2\frac{5}{6}\), what must you do first? (a) Subtract the whole numbers directly (b) Borrow 1 from the whole number and regroup (c) Add the fractions together (d) Convert both mixed numbers to whole numbers
Solution:
Ans: (b) Explanation: Since \(\frac{1}{6}\) is smaller than \(\frac{5}{6}\), you cannot subtract directly. You must borrow 1 from the whole number 5, making it 4, and convert that 1 into \(\frac{6}{6}\). Then \(5\frac{1}{6}\) becomes \(4\frac{7}{6}\).
Q5: What is \(3\frac{5}{8} + 1\frac{7}{8}\)? (a) \(4\frac{12}{8}\) (b) \(5\frac{1}{2}\) (c) \(5\frac{4}{8}\) (d) \(4\frac{6}{8}\)
Solution:
Ans: (b) Explanation: Add the whole numbers: \(3 + 1 = 4\). Add the fractions: \(\frac{5}{8} + \frac{7}{8} = \frac{12}{8} = 1\frac{4}{8} = 1\frac{1}{2}\). Add to the whole number: \(4 + 1\frac{1}{2} = 5\frac{1}{2}\).
Q6: What is \(6\frac{2}{5} - 3\frac{4}{5}\)? (a) \(3\frac{3}{5}\) (b) \(2\frac{3}{5}\) (c) \(2\frac{4}{5}\) (d) \(3\frac{2}{5}\)
Solution:
Ans: (b) Explanation: Since \(\frac{2}{5} < \frac{4}{5}\),="">borrow 1 from 6, making it 5. Convert 1 to \(\frac{5}{5}\), so \(6\frac{2}{5} = 5\frac{7}{5}\). Now subtract: \(5 - 3 = 2\) and \(\frac{7}{5} - \frac{4}{5} = \frac{3}{5}\). The answer is \(2\frac{3}{5}\).
Q7: Which pair of mixed numbers has a sum greater than 10? (a) \(4\frac{1}{2} + 5\frac{1}{3}\) (b) \(3\frac{2}{5} + 6\frac{1}{5}\) (c) \(5\frac{3}{4} + 4\frac{1}{2}\) (d) \(2\frac{1}{6} + 7\frac{2}{6}\)
Q8: If you simplify \(7\frac{4}{6} - 3\frac{1}{6}\), what is the answer in simplest form? (a) \(4\frac{3}{6}\) (b) \(4\frac{1}{2}\) (c) \(4\frac{1}{3}\) (d) \(5\frac{1}{2}\)
Solution:
Ans: (b) Explanation: Subtract: \(7 - 3 = 4\) and \(\frac{4}{6} - \frac{1}{6} = \frac{3}{6}\). Simplify \(\frac{3}{6} = \frac{1}{2}\). The answer is \(4\frac{1}{2}\).
Section B: Fill in the Blanks
Q9: When adding mixed numbers, if the sum of the fractions is an improper fraction, you must convert it to a __________ and add it to the whole number part.
Solution:
Ans: mixed number Explanation: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. You convert it to a mixed number and add the whole number part to the existing whole numbers.
Q10: To subtract \(5\frac{1}{8} - 2\frac{5}{8}\), you need to __________ 1 from the whole number 5 because the fraction \(\frac{1}{8}\) is smaller than \(\frac{5}{8}\).
Solution:
Ans: borrow Explanation: When the fraction in the first mixed number is smaller than the fraction in the second mixed number, you must borrow 1 from the whole number and regroup it as an equivalent fraction.
Q11: The sum of \(2\frac{3}{10} + 4\frac{7}{10}\) is __________.
Solution:
Ans: \(7\) or 7 Explanation: Add the whole numbers: \(2 + 4 = 6\). Add the fractions: \(\frac{3}{10} + \frac{7}{10} = \frac{10}{10} = 1\). Total: \(6 + 1 = 7\).
Q12: When both mixed numbers have the same denominator, you can add or subtract the fractions __________.
Solution:
Ans: directly Explanation: When fractions have the same denominator, you simply add or subtract the numerators and keep the denominator the same.
Q13: The difference of \(8\frac{5}{6} - 3\frac{1}{6}\) is __________.
Solution:
Ans: \(5\frac{4}{6}\) or \(5\frac{2}{3}\) Explanation: Subtract the whole numbers: \(8 - 3 = 5\). Subtract the fractions: \(\frac{5}{6} - \frac{1}{6} = \frac{4}{6}\). The answer is \(5\frac{4}{6}\), which simplifies to \(5\frac{2}{3}\).
Q14: After adding \(1\frac{5}{8} + 2\frac{7}{8}\), the improper fraction \(\frac{12}{8}\) simplifies to the mixed number __________.
Solution:
Ans: \(1\frac{4}{8}\) or \(1\frac{1}{2}\) Explanation: The improper fraction \(\frac{12}{8}\) equals \(1\frac{4}{8}\), which simplifies to \(1\frac{1}{2}\).
Section C: Word Problems
Q15: Sarah baked a cake and used \(2\frac{3}{4}\) cups of flour for the batter and \(1\frac{1}{4}\) cups of flour for the frosting. How many cups of flour did she use in total?
Solution:
Ans:
Add the whole numbers: \(2 + 1 = 3\)
Add the fractions: \(\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1\)
Total: \(3 + 1 = 4\) Final Answer: 4 cups of flour
Q16: Jason ran \(5\frac{2}{5}\) miles on Saturday and \(3\frac{4}{5}\) miles on Sunday. How many more miles did he run on Saturday than on Sunday?
Solution:
Ans:
Subtract the whole numbers: \(5 - 3 = 2\)
Subtract the fractions: \(\frac{2}{5} - \frac{4}{5}\) (need to borrow)
Borrow 1 from 2, making it 1, and convert 1 to \(\frac{5}{5}\)
So \(2\frac{2}{5} = 1\frac{7}{5}\)
Now: \(1 - 0 = 1\) and \(\frac{7}{5} - \frac{4}{5} = \frac{3}{5}\) Final Answer: \(1\frac{3}{5}\) miles
Q17: A recipe calls for \(3\frac{1}{3}\) cups of sugar. Maria only has \(1\frac{2}{3}\) cups of sugar. How much more sugar does she need?
Solution:
Ans:
Subtract: \(3\frac{1}{3} - 1\frac{2}{3}\)
Since \(\frac{1}{3} < \frac{2}{3}\),="" borrow="" 1="" from="" 3,="" making="" it="">
Convert 1 to \(\frac{3}{3}\), so \(3\frac{1}{3} = 2\frac{4}{3}\)
Now: \(2 - 1 = 1\) and \(\frac{4}{3} - \frac{2}{3} = \frac{2}{3}\) Final Answer: \(1\frac{2}{3}\) cups of sugar
Q18: A board is \(8\frac{3}{8}\) feet long. If Tom cuts off \(2\frac{5}{8}\) feet, how long is the remaining board?
Solution:
Ans:
Subtract: \(8\frac{3}{8} - 2\frac{5}{8}\)
Since \(\frac{3}{8} < \frac{5}{8}\),="" borrow="" 1="" from="" 8,="" making="" it="">
Convert 1 to \(\frac{8}{8}\), so \(8\frac{3}{8} = 7\frac{11}{8}\)
Now: \(7 - 2 = 5\) and \(\frac{11}{8} - \frac{5}{8} = \frac{6}{8} = \frac{3}{4}\) Final Answer: \(5\frac{3}{4}\) feet
Q19: Emma walked \(2\frac{5}{6}\) miles to the library and then \(1\frac{5}{6}\) miles to the park. What is the total distance she walked?
Solution:
Ans:
Add the whole numbers: \(2 + 1 = 3\)
Add the fractions: \(\frac{5}{6} + \frac{5}{6} = \frac{10}{6}\)
Convert \(\frac{10}{6}\) to a mixed number: \(\frac{10}{6} = 1\frac{4}{6} = 1\frac{2}{3}\)
Total: \(3 + 1\frac{2}{3} = 4\frac{2}{3}\) Final Answer: \(4\frac{2}{3}\) miles
Q20: A water tank had \(10\frac{1}{4}\) gallons of water. After using \(3\frac{3}{4}\) gallons for watering plants, how much water is left in the tank?
Solution:
Ans:
Subtract: \(10\frac{1}{4} - 3\frac{3}{4}\)
Since \(\frac{1}{4} < \frac{3}{4}\),="" borrow="" 1="" from="" 10,="" making="" it="">
Convert 1 to \(\frac{4}{4}\), so \(10\frac{1}{4} = 9\frac{5}{4}\)
Now: \(9 - 3 = 6\) and \(\frac{5}{4} - \frac{3}{4} = \frac{2}{4} = \frac{1}{2}\) Final Answer: \(6\frac{1}{2}\) gallons
The document Worksheet (with Solutions): Adding and Subtracting Mixed Numbers is a part of the Grade 4 Course Math Grade 4.
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